Classification of Hamiltonian Non-Abelian Painlevé Type Systems

All Hamiltonian non-abelian Painlevé systems of P1-P6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\mathrm{P_{1}}\,}}-{{\,\mathrm{P_{6}}\,}}$$\end{document} type with constant coefficients are found. For P1-P5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\mathrm{P_{1}}\,}}-{{\,\mathrm{P_{5}}\,}}$$\end{document} systems, we replace an appropriate inessential constant parameter with a non-abelian constant. To prove the integrability of new P3′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\mathrm{P_{3}^{\prime }}\,}}$$\end{document} and P5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\mathrm{P_{5}}\,}}$$\end{document} systems thus obtained, we find isomonodromic Lax pairs for them.